1. Field of the Invention
The present invention relates generally to the field of petroleum reservoir simulation history matching. More specifically, the present invention relates to the field of computing approximate static well pressures for one or more arbitrary shaped wells in both homogeneous and heterogeneous reservoirs.
2. Description of Related Art
Major oil companies, independent oil companies, small oil companies, and oil reservoir management consultants use reservoir simulators routinely in reservoir management. More specifically, oil field reservoir simulators are often used by oil industry professionals and oil companies to design new oil fields, determine efficient and productive drilling schedules, select optimum well locations, estimate surface facility timings, and design recovery methods. History matching is a key phase in a reservoir simulator as it serves to justify the model generated by a particular reservoir simulator as a predictive tool by matching key reservoir simulation variables to corresponding measured oil field data. In history matching, several key variables can be matched to measured quantities from field data to verify a particular simulator model as a predictive tool such as water cuts, gas oil ratios, and static well pressure.
Static well pressure, for example, is a particularly useful variable to verify a reservoir simulator model as a predictive tool, and accordingly, static well pressure receives prime attention during a history match. Specifically, the pressure variable is not only an indicator of reservoir energy, it is also indicative of a variety of other factors affecting the reservoir performance. Accordingly, many reservoir simulators are matched for static well pressures first before matching the other variables.
During a history match, for example, simulator computed well pressures can be matched against the measured static well pressures from measured field data. The measured static well pressures are generally obtained from pressure build-up tests and stored in corporate databases as field data. These pressure build-up tests are conducted at certain intervals during the life of the well. Ideally, a reservoir simulator can be used, for example, to simulate a pressure build-up test to thereby compute static well pressures at each simulated time interval that can be history matched to measured well pressures at each corresponding time interval to verify the integrity of the reservoir simulator as a predictive tool. The timing and number of such build-up tests, however, generally does not match the number of simulated static well pressures because the reservoir simulator calculates a static well pressure at each simulated time step or iteration, to an extent that the reservoir time steps vastly outnumber the number of actual build-up tests. As such, a one-to-one ratio in the time domain is unlikely when measured well data is history matched with reservoir simulator data.
As noted above, pressure build-up tests can be used to compute the static well pressure for a particular well, and for each pressure build-up test, the static well pressure can be measured and recorded in a field data database. These pressure build-up tests, however, may only be conducted once each month, and as such, only one static well pressure reading for each month will be available in the recorded field data for history matching. Conversely, a reservoir simulator can generate, for example, a static well pressure at each iteration or step, and such steps can vastly outnumber the number of observed, measured static well pressures of a particular well. Therefore, the time steps or iterations of a particular reservoir simulator is generally adjusted and reduced significantly to better approximate the actual frequency of build-up tests conducted during the history of a particular reservoir.
In practice, reservoir simulators use pore volume averaged grid block pressures over the grid blocks in which the well is perforated (i.e., perforated cells) to approximate static pressure. While this approximation may be somewhat reasonable for very large grid blocks, the inventors have recognized, however, that it is not a good approximation for smaller grid blocks when locally refined grids around the well are used, as the error becomes significant and must be corrected. Various correction factors are known in the art to correct static pressure estimated using pore volume averaged grid block pressures for perforated cells to match measured pressure build-up test driven static well pressures. These correction factors, however, are developed principally for vertical wells, and accordingly, fail to function appropriately when applied to multi-lateral wells, maximum reservoir contact welts, and many newer types of wells with complex shapes. Nonetheless, particularly in scenarios where correction factors fail to function appropriately, such as with wells of complex shapes, interpolation techniques can be used to accommodate the difference in build-up test times and simulator time steps. The use of interpolation techniques, however, results in an inefficient use of computer processing resources and can result in or otherwise require wrongfully introducing permeability modifiers to match the pressures when no real need exists for any modification of the reservoir properties.